J. Aust. Math. Soc.  75 (2003), 181-191
On finite $\mathcal{T}$-groups

A. Ballester-Bolinches
  Departament d'Àlgebra
  Universitat de València
  Dr. Moliner, 50
  E-46100 Burjassot (València)
  Spain
  adolfo.ballester@uv.es
and
R. Esteban-Romero
  Departament de Matemàtica Aplicada
  Universitat Politècnica de València
  Camì de Vera, s/n
  E-46022 València
  Spain
  resteban@mat.upv.es


Abstract
Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.
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